Papers by Maciej Machowiak
Proceedings of the 7th International Euro Par Conference Manchester on Parallel Processing, Aug 28, 2001
Malleable tasks consist in considering the tasks of a parallel program as large computational uni... more Malleable tasks consist in considering the tasks of a parallel program as large computational units that may be themselves parallelized. In this paper we investigate the problem of scheduling a set of n independent malleable tasks on a m processors system, starting from the continuous version of the problem.
Bulletin of the Polish Academy of Sciences Technical Sciences, 2014
The problem of scheduling n tasks in a multiprocessor system with m processors to minimize the ma... more The problem of scheduling n tasks in a multiprocessor system with m processors to minimize the makespan is studied. Tasks are malleable, which means that a task can be executed by several processors at a time, its processing speed depends on the number of allocated processors, and a set of processors allocated to the same task can change over time. The processing speed of a task is a strictly increasing function of the number of processors allocated to this task. The earlier studies considered the case n ≤ m. This paper presents results for arbitrary n and m including characterizations of a feasible domain and an optimal solution, polynomial time algorithms for strictly increasing convex and concave processing speed functions, and a combinatorial exponential algorithm for arbitrary strictly increasing functions.
Lecture Notes in Computer Science, 2001
Malleable tasks consist in considering the tasks of a parallel program as large computational uni... more Malleable tasks consist in considering the tasks of a parallel program as large computational units that may be themselves parallelized. In this paper we investigate the problem of scheduling a set of n independent malleable tasks on a m processors system, starting from the continuous version of the problem.
Computational Methods in Science and Technology, 2000
In the paper, the problem of scheduling a set of n malleable tasks on m parallel computers is con... more In the paper, the problem of scheduling a set of n malleable tasks on m parallel computers is considered. The tasks may be executed by several processors simultaneously and the processing speed of a task is a function of the number of processors alloted. The problem is motivated by real-life applications of parallel computer systems in scientific computing of highly parallelizable tasks. Starting from the continuous version of the problem (i. e. where the tasks may require a fractional part of the resources), we propose a general approximation algorithm with a performance guarantee equal to 2. Then, some improvements are derived that lead to a very good average behavior of the scheduling algorithm.
Journal of the Operational Research Society, 2011
We study the problem of allocating berths to incoming ships and assigning the necessary quay cran... more We study the problem of allocating berths to incoming ships and assigning the necessary quay cranes to the ships at a port container terminal. We formulate the problem as the moldable task scheduling problem by considering the tasks as ships and processors as quay cranes assigned to the ships based on the observation that the berthing duration of a ship depends on the number of quay cranes allocated to it. In the model, the processing speed of a task is considered to be a non-linear function of the number of processors allocated to it. We present a suboptimal algorithm that obtains a feasible solution to the discrete version of the problem from the continuous version, that is, where the tasks may require fractional quantities of the resources. We conducted computational experiments to evaluate the performance of the algorithm. The computational results show that the average behaviour of the algorithm is very good.
Annals of Operations Research, 2000
Annals of Operations Research, 2000
IEEE Transactions on Computers, 2000
The problem of optimal scheduling n independent malleable tasks in a parallel processor system is... more The problem of optimal scheduling n independent malleable tasks in a parallel processor system is studied. It is assumed that an execution of any task can be preempted and the number of processors allocated to the same task can change during its execution. We present a rectangle packing algorithm, which converts an optimal solution for the relaxed problem, in which the number of processors allocated to a task is not required to be integer, into an optimal solution for the original problem in OðnÞ time.
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Papers by Maciej Machowiak